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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−x+3f(x) = -x + 3\newlineg(x)=3x2g(x) = 3x^2\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−x+3f(x) = -x + 3\newlineg(x)=3x2g(x) = 3x^2\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______
  1. Identify Formula: Identify the formula for (f∗g)(x)(f * g)(x).(f∗g)(x)(f * g)(x) is the product of f(x)f(x) and g(x)g(x).(f∗g)(x)=f(x)∗g(x)(f * g)(x) = f(x) * g(x)
  2. Given Functions: We have:\newlinef(x)=−x+3f(x) = -x + 3\newlineg(x)=3x2g(x) = 3x^2\newlineTo find (f∗g)(x)(f * g)(x), we need to multiply f(x)f(x) by g(x)g(x).\newline(f∗g)(x)=(−x+3)∗(3x2)(f * g)(x) = (-x + 3) * (3x^2)
  3. Distribute Terms: Distribute 3x23x^2 to each term in (−x+3)(-x + 3).
    (f∗g)(x)=(−x∗3x2)+(3∗3x2)(f * g)(x) = (-x * 3x^2) + (3 * 3x^2)
  4. Perform Multiplication: Perform the multiplication.\newline(f⋅g)(x)=−3x3+9x2(f \cdot g)(x) = -3x^3 + 9x^2

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